Analyzing the Impact of Magnetic Field, Squeezing, and Volume Fraction on Magnetohydrodynamic Nanofluid Flow Using a Differential Transform Method

The study aims to analyze the characteristics and behavior of heat and mass transfer (H-MT) in an unsteady magnetohydrodynamic (MHD) flows of nanofluids that are squeezed between two parallel plates. The base fluid used in the study is water, and silicon dioxide is taken as the nanoparticle material. The main PDEs are appropriately transformed into ODEs. The reduced equations are then evaluated using the DTM, which is a strong numerical procedure for solving nonlinear ODEs. The study focuses on the impact of several parameters on all profiles, including magnetic field parameter, squeezing parameter, and volume fraction on all profiles. It is also addressed how the Schmidt number affects the concentration profile and how the Eckert, Prandtl, and Schmidt numbers affect temperature and chemical reactions. The results are presented graphically, and the accuracy and effectiveness of the DTM method are authenticated through a comparison with existing literature. Moreover, the skin friction coefficient, Nusselt number, and Sherwood number are also compared with the numerical method, and a comparative study confirms the accuracy of the DTM method. The novelty of this study is to provide new insights into the effect of magnetic field, squeezing effects, and nanoparticle volume fraction on H-MT characteristics. The comparative validation with numerical results further establishes the robustness of DTM in addressing complex nanofluid flow problems. The study’s importance is highlighted by its detailed investigation of key physical parameters affecting H-MT, which enhances the understanding of nanofluid behavior in confined geometries. The outcomes show that as the magnetic field’s intensity and squeezing parameter values increase, temperature decreases. While as the volume fraction increases, the temperature rises. As the squeezing parameter increases, concentration rises as well. Also, the Schmidt number has an inverse relationship with concentration. The findings of this study could be useful in optimizing various industrial processes involving nanofluid flows and contribute to the advancement of the field of fluid dynamics.